Study of viscoelastic effect on the frequency shift of microcantilever chemical sensors

Microcantilevers coated with a chemically sensitive layer are increasingly being used in chemical detection systems. The sensitive coating, often a polymer, absorbs specific molecules, which can be detected by monitoring the shift in the mechanical resonant frequency. Usually, the frequency shift resulting from molecular absorption is interpreted as a mass loading effect. However, mass loading is not the only effect that has an impact on the frequency shift; the viscoelastic properties of the sensitive coating also are affected by the sorption process. Sorption-induced modulus changes are typically difficult to characterize. However, it is known that the sorption of analyte molecules in a polymer coating results in the plasticization of the coating. In most cases, the polymer becomes more rubbery with increasing concentration of analyte molecules, i.e., the coating becomes softer with increasing loss modulus, and the storage modulus decreases. Using a new analytical model developed for the resonant frequency expression of a hybrid microcantilever (elastic base and viscoelastic layer), the effects of the modification of the storage and loss moduli of the sensitive layer on the resonant frequency are examined. The main conclusion of this analytical study is that, even if the sensitive coating moduli are small compared to the base cantilever's Young's modulus, the effect of the change in the viscoelastic coating properties could contribute significantly to the overall frequency shift (8-23% in the simulations depending on the coating thickness, with even higher contributions for other sets of problem parameters).